I think you already know the answer to your question. It’s over. She’s heard it all before. She doesn’t trust you to be faithful. She doesn’t believe that the meds or the addiction made you do it. Cheating with an underage kid was the last straw. Now she doesn’t trust you with your kids either.
The best thing you can do is focus on your own therapeutic work. It’s possible that if you are successful in making substantive change, you’ll be able to have at least a cooperative relationship with their mother for the kids’ benefit, if not a cordial one.
Talk to your lawyer about options for supervision so you don’t lose touch with your children. Talk to your therapist about how to explain your divorce to your children in a way that doesn’t put the blame on their mother. Take treatment seriously for your own healing and growth.
I wish you well.